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We consider the problem of determining the class of continuous-time dynamical systems that can be globally linearized in the sense of admitting an embedding into a linear system on a higher-dimensional Euclidean space.
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Linearization and global dynamics
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Linearization in the large of nonlinear systems and Koopman operator spectrum
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T Tao · 2017
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On the universality of the incompressible Euler equation on compact manifolds
T Tao · 2018
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J Levine and R Marino · 1986
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Krzysztof Kowalski and Willi-Hans Steeb · 1991
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K Sakamoto · 1994
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Locally finite and locally nilpotent derivations with applications to polynomial flows, morphisms and 𝒢 a \mathscr{G}_{a} -actions. II
A van den Essen · 1994
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Smooth invariant manifolds and normal forms
I U Bronstein and A Y Kopanskiĭ · 1994
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Global linearization and fiber bundle structure of invariant manifolds
J Eldering, M Kvalheim, and S Revzen · 2018
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Deep learning for universal linear embeddings of nonlinear dynamics
B Lusch, J N Kutz, and S L Brunton · 2018
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Smoothing Lyapunov functions
A Fathi and P Pageault · 2019
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Spectrum of the Koopman operator, spectral expansions in functional spaces, and state-space geometry
I Mezić · 2020
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On the universality of the incompressible Euler equation on compact manifolds, II. Non-rigidity of Euler flows
T Tao · 2020
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Koopman operator, geometry, and learning of dynamical systems
I Mezić · 2021
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Existence and uniqueness of global Koopman eigenfunctions for stable fixed points and periodic orbits
M D Kvalheim and S Revzen · 2021
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Challenges in dynamic mode decomposition
Z Wu, S L Brunton, and S Revzen · 2021
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Modern Koopman theory for dynamical systems
S L Brunton, M Budišić, E Kaiser, and J N Kutz · 2022
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Canonical forms for polynomial systems with balanced super-linearizations
M-A Belabbas · 2022
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Visible and hidden observables in super-linearization
M-A Belabbas · 2022
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A sufficient condition for the super-linearization of polynomial systems
M-A Belabbas and X Chen · 2023
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On the non-existence of immersions for systems with multiple omega-limit sets
Z Liu, N Ozay, and E D Sontag · 2023
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An h h -principle for embeddings transverse to a contact structure
R Cardona and F Presas · 2024
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J Ko and M-A Belabbas · 2024
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Data-driven linearization of dynamical systems
G Haller and B Kaszás · 2024
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Properties of immersions for systems with multiple limit sets with implications to learning Koopman embeddings
Z Liu, N Ozay, and E D Sontag · 2025
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